This operator is crucially important to make the loop equations closed: \(z\) -dependence of \(\rho \)  depends on the action of \(\check{R}_z\) . At the same time, it affects the equation only “a little”: the corresponding piece is a polynomial of finite degree in \(z\) , while the function \(\rho ^{(1)}(z)\)  is essentially non-polynomial (in fact, one would better consider \(\rho ^{(1)}(z)dz\)  as a 1-differential [1]}, [2]}, [3]}, [4]}, however, we do not discuss this kind of subtleties in the short review).
